Relation between the medical good and the related good

Question:

Use the following to answer a-e. Please show all work in as much detail as possible. Assume Q is the quantity demanded for medical care services. The linear industry demand function takes the form

Q = a +bp +cM +dPr

where:

P = the price of the medical care
M = median household income
Pr = the price of a related good

dependent variable: Q R-square F-ratio P-value on F
0.8118 28.75 0.0001

Observations: 24

Variable PARAMETER ESTIMATE std error T-Ratio P-value

INTERCEPT 68.38 12.665 5.41 0.0001
P -6.5 3.15 -2.06 0.0492
M 0.13926 0.0131 10.63 0.0001
PR -10.77 2.45 -4.4 0.0002

a. Is the sign of ^b (hat over b) as would be predicted theoretically? Why/

b. What does the sign of ^c(hat over c) imply about the good?

c. what does the sign of ^d imply about the relation between the medical good and the related good R?

d. Are the parameter estimates ^a, ^b, ^c, and ^d statistically significant at the 5% level of significance?

e. Using the values P = 225, M= 24,000, and Pr =60, calculate the estimates of

(1) the price elasticity of demand (^Ed)
(2) the income elasticity of demand (^Ey)
(3) the cross-price elasticity (^Ec)

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